The general position number of Cartesian products involving a factor with small diameter
作者：
Highlights：
• The gp-number is determined for the Cartesian product of a tree and a complete graph.
• The gp-numbers are demonstrated for the Cartesian product of a complete graph with a cycle and that of a complete multipartite graph with a path, respectively.
• An upper bound on the gp-number is proved for the Cartesian products of any two connected graphs G and H, and the bound is sharp if G and H have diameters at most 2. Moreover, the equality holds if and only if G and H are both generalized complete graphs.
摘要
•The gp-number is determined for the Cartesian product of a tree and a complete graph.•The gp-numbers are demonstrated for the Cartesian product of a complete graph with a cycle and that of a complete multipartite graph with a path, respectively.•An upper bound on the gp-number is proved for the Cartesian products of any two connected graphs G and H, and the bound is sharp if G and H have diameters at most 2. Moreover, the equality holds if and only if G and H are both generalized complete graphs.
论文关键词：General position set,Cartesian product,General position number
论文评审过程：Received 9 November 2020, Revised 6 March 2021, Accepted 12 March 2021, Available online 26 March 2021, Version of Record 26 March 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126206
